mlsanityData to 14 Oct 2026

Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems

arXiv 2504.03069 ↗First posted 3 Apr 2025math.OC cs.AI cs.NAcited by 3

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Abstract (arXiv)

This paper studies properties of fixed points of generalised Extra-gradient (GEG) algorithms applied to min-max problems. We discuss connections between saddle points of the objective function of the min-max problem and GEG fixed points. We show that, under appropriate step-size selections, the set of saddle points (Nash equilibria) is a subset of stable fixed points of GEG. Convergence properties of the GEG algorithm are obtained through a stability analysis of a discrete-time dynamical system. The results and benefits when compared to existing methods are illustrated through numerical examples.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 9 of its 29 references that are in the map. First posted on arXiv 3 Apr 2025.

Builds on

9 of 29 references.

References · 9

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2017Deep Decentralized Multi-task Multi-Agent Reinforcement Learning under Partial Observabilitycited by 148
  3. 2018The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimizationcited by 101
  4. 2020Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimizationcited by 96
  5. 2021Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Gamescited by 69
  6. 2020The limits of min-max optimization algorithms: convergence to spurious non-critical setscited by 50
  7. 2022Stochastic Gradient Descent-Ascent: Unified Theory and New Efficient Methodscited by 37
  8. 2021Direct-Search for a Class of Stochastic Min-Max Problemscited by 7
  9. 2023Two-timescale Extragradient for Finding Local Minimax Pointscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approachcited by 2
  2. 2026On the Stability Connection Between Discrete-Time Algorithms and Their Resolution ODEs: Applications to Min-Max Optimisationcited by 1
  3. 2026From Cursed to Competitive: Closing the ZO-FO Gap via Input-to-State Stabilitycited by 0